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Challenges in characterization of concentrated suspensions
c0,,0s
AND ELSEVIER
Colloids and surf~.... A: Physicochemic~d~mdEngineeringAspects 13311998) 143 150
A
~UR~AC~
Challenges in characterization of concentrated suspensions S. C h a n d e r 115 th,.vler Building. Penn Stare Unirersitr. University Park PA 168¢)2. USA
Accepted I April 1997
Abstract With a decrease in perticle size below I rLm Ihe role of surfaces and interlhcial phenomena dominates the properties of powders in liquids. A knowledge of properties of the system is often desired to develop predictive strategies to control the state of dispersion and aggregation of powders. To obtain the desired stability and rheology of suspensions, an adjustment of both physical and chemical variables might be reqnired. The success of such an approach depends on the ability to predict correctly the system response fron't characteristics of the powder and suspending medium. Several traditiomd methods of characterization depend upon measurements in dilute suspensions, whereas most applications deal with processing and transport of dispersions at htrge particle loading (percent solids). Challenges in rchning properties measured in dihae suspensions to predict lhc behavior of concentrated suspensions will be discussed. golh thermodynamic or equilibrium, and kinetic or rate elfects are considered. ~o 1998 Elsevier Science B.V. KO'wordw Concentrated snspensions; Characterization: Dynamic properties: Stability
I. Concentrated suspensionsIdefinitions The terlrl "concentrated suspension" is often used without a clear definition. In many cases the practical definition is user-dependent and not alw',tys usefal across different fields of interest. At one extreme, n suspension may be cotlsidered dilute if the thermal motion of the particle predominates over the effect imposed by interparticle forces [ 1,2]. As a result, the particle translational motion is large compared to the range in which interparticle forces are significant. In dilute suspensions, colloid properties can be described in terms of two-body inter;~ctions between a pair of particles. In these "'dilute" systems particles move independently and they do not "~see'" each other except for a chance collision. Such systems are seldom of prnetieal interest, however. At the other end of the spectrum is the so-called "'ordered" suspension in which particles occupy specific sites with respect 0927-7757;9s sI9.110t, 1998Elsevier:~cienceB.V. All rights reserved. PII $1t927-7757197 )tilt 134-9
to each other. S'~c~: suspensions are conveniently referred to as "'solid" suspensions. The properties of such suspension,~ could be time invariant if interparticle forces do not change with time. In between the above extreme cases of "'dilute" and "'solid" suspensions are systems which are loosely defined as "'concentrated". In these systems, which are of most practical importance in the industry, particle interactions are many-body in nature and the translational motion of the particles is restricted [3]. The particles "'see" each other within a short time scale when compared with "'dilute" suspensions. The properties of such systems are time-dependent showing both spatial and temporal distributions. Theoreticnl!y. the radial distribution of particles around a central particle can be used to describe microstructure in ~uch suspensions. Determination of such a distribution is not a trivial task, however. In many practical applications, where the aim is to control various properties o f
144
,~ ( 7la~tder ('o]loi~Ll"StctJktct.s A: Ph.rsh'l~rhtwt, Erie. A~¢cts 133 ~ 199~) 143 15(1
the system, the goal of an investigator is to relate particle properties to macroscopic properties, such as osmotic pressure, stability or rheology. The usual expression for mean interparticle spacing H in a suspension is
where D is particle diameter, ~ is volume fraction, and ~,, is volume fraction at maximum packing. For such a calculation, all particles are assumed to be spherical and of same size. The interpartiele spacing H for particle of various diameters is plotted as a function of volume fraction in Fig. I using the above relation. It can be seen that the interparticle spacing is less than the particle diameter in suspensions of most practical interest. Tile value of ~,~ depends on the packing of particles in the suspension. As a limiting case, if the particles are arranged ill a close-packing structure, for example face-centered cubic, the value of ~Pm is 0.74 and the value of ¢]J at which the distance of separation between nearest neighbors is equal to particle diameter is 0.093. On the other hand, if the particles are arranged in a simple cubic arrangement in the liquid, the wduc of q~ for a similar interparticle spacing is 0.066. This difference arises because tile wdue of q~m ill a simple
cubic arrangement is 0.524. In other words, the average distance of separation between particles is equal to the particle diameter in a range of volume fractions, which is a fnnction of structure of the suspension. Further differences between the definition of dilute and concentrated suspensions could arise due to the particle shape effects and colloid interactions between the particles. The effect of colloid forces can be incorporated in the case of "'stable" suspensions by considering a modified particle diameter based on the "'sphere of influence" of the particle. To define the sphere of influence a knowledge of interparticle lbrccs is required, however. Differences in structural arrangement of particles in a suspension could arise when attractive and weakly repulsive Ibrces are present between the particles. In such a case the arrangement of particles in the suspension becomes a f.mction of time and is determined by kinetics of coagulation. Thus, the definition of dilute and concentrated suspensions is a ftmction of the arrangement of particles in the suspension, which in turn depends on interparticle forces. The effect of interparticle forces are discussed in the paragraphs that lbllo~. It was discussed in the previous paragraph that, at volume fractions gceuter than a critical value, a transhtting particle will collide with the particle in
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s, ('bander ; ('olloM.v Surfitce~" A. ?'l)wtcochent Eng. Aspects 133 (1998) 143-150
its immediate vicinity. A force will be transmitted from one particle to another after such an event. The magnitude of such a force would follow rules of momentum transfer but will also depend on mutual interactions between the particles. Electrical double layer interactions, van der Waals forces and solvation effects are known to influence t~roperties of concentrated suspensions, but their effect is rarely incorporated in quantitative theories of macroscopic properties of such systems. Definite forms of momentum balances, wflid over a whole range of particle sizes, solids concentration or particulate density, and interparticle interactions are not available. All existing attempts to lbrmulate a theory usually involve ad hoc assumptions, some of which may be controversial. At volume fractions corresponding to interparticle distances smaller than the particle diameter, the probability of multi-body particle interactions increases and the forces of interacti~,n between particles play a dominant role in determining the system properties. Such interactions cannot be ignored for a "+concentrated" suspension, however. Auzerais et hi. [4] presented a detailed model of the settling of concentrated snspensions, but had to linfit their calculations to two extreme cases: the hard sphere model, and the flocculated model. The effect of distance-dependent magnitude of interparticlc forces could not be taken into account. Although used as the most connnou control variable, the volume fraction alone is not sufficient to describe the properties of a concentrated suspension. To illustrate this limitation, consider the coagulation time constant (defined as the time required for a system to decrease the number of particles to half its initial valuet as a function of volume fraction for particles of various sizes. The values are given in Fig. 2 for a rapidly coagulating system. The coagulation time constant can vary from a few milliseconds to several hours, depending on particle size and volume fraction. Thus, the definition of a concentrated suspension must incorporate, at the very least, volume fraction, particle size (distribution), and interparticle forces. 2. Characterization ufa disperse system Adequate characterization of a disperse system is important if one needs to develop ways to
145
predict system properties and relate them to performance. A system of disperse particles might be characterized by properties of the disperse phase(s), continuous phase, interfacial properties and the colloid properties. A list of these properties is given in Table I. Although several methods are available to determine various properties under isolated conditions, difficulties remain for measurements in concentrated suspensions. As an example, in many industrial systems the state of aggregation of primary particles is most difficult to control and measure. In principle, the aggregates can be characterized by the size distribution, density, strength and rate of their formation. However, most modern methods for determining size distributions do not distinguish between aggregates of fine particles and course particles. Since disperse, continuous and interracial properties can be measured routinely by traditional methods, further discussion in this article is limited to stability and rheology. 2. I. Stabili(v
Methods of characterizing stability of concentrated dispersions have not been standardized, and a large variation in techniques and methodology exists in the literature. The simplest way to determine stability is to measure sediment volume, sediment density or sediment height
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Table 1 Paralnet¢ls for ch~lraClerizinga s3~tenl of dispersed pill'lides I)is~.rse phase properties
Size dislribution Particle shape I)ensil,, Surl~lc¢ ¢llcrgy nolntll~cll¢il~
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Percent solids Stabilil} Rhcoh~gy l.ight st-ant:ring
riot nnifornl and the sediment migllt have a nonnnilbrm density. The results after consolidation in a centrifttge are given in Fig. 3 [6] as an illustralion. Ahhough additional information about the properties of the system could he obtained from measuring the rate of settling, such tests are not ordinarily pertbrmed tbr eoncenlrated suspensions and the available data are meager, Pressure liltration is another method used by some investigators to describe the settling behavior of suspensions [7]. Thc most c o m m o n approach is to measure equilibrium cake height as a fimction of pressure. The results after consolidation by pressure filtration are given Fig. 4 [6]. Important differences between the results of centrifugal settling and pressure filtration are noticeable, hi centrifugal settling tile packing density varies linearly witb pressure when the two quantities are plotted on logarithmic scales. In contrast, the packing density wtried with the logarithm of the applied pressure in pressure filtration. Obviously, important differences must exist in the two cases. The reasons for such differences were not discussed by the investigators and are not obvious. In centrilugal settling the pressure ranges from about a few deci- to se~'eral kilo-pascals, whereas it, pressure
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filtration it ranges from a few deci- to several mega-pascals, The packing behavior of particles in the suspension could change with increase in pressure but the type of change that could occur rcntaius to be established. 2.2. D t'mu,icpr~qwrtie.~
Rheok~gy properties c~m b~. u~.ed to dc~cribe the dynamic properties of concentrated suspensions under flow conditions. These properties can be
147
investigated using steady state, constant stress (creep) or oscillatory measurements [8]. Rheology properties of the suspensions vary considerably with change in interparticle forces. As a result, they are often grouped into different categories based on hard sphere interaction, double layer repulsion, steric stabilization, weak attraction {weakly flocculated suspensions), and strong attraction {strongly flocculated suspensions). Such a sub-division is obviously arbitrary and arises from the lack of a rigorous theory that can incorporate interaction between particles into rheology theories. Other difficulties arise in determination of rheology properties. For non-Newtonian systems, the properties often depend on history of the dispersion and segregation of particles in the test cell. Using an NMR imaging technique, Mondy and Graham [9] demonstrated that a 60 vol.% suspension containing bidisperse spheres segregated into concentric cylinders with alternating coarse and fine particles. Similar problems could arise in a rheology test cell if the suspension contains a wide distribution of particle sizes. Slip near the walls of the test cell is another well recognized major problem in measuring rheology properties of dense slurries.
3. Preparation of dispersions 8O ~'~
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Preparation of a dispersion l¥om a dry powder is the first step in many practicab-applications and laboratory investigations. Though technically important, this feature if often ignored in many discussions involving concentrated suspensions. Dispersions can be prepared either by precipitation methods or by comminution of coarse particles. Although a detailed discussion of either of these topics is beyond the scope of this article, a brief commentary is included because the dispersion properties play an important role in both cases. In comminution, production of fine particles could result in an increase in viscosity of the suspension, decreasing stress transfer and effectiveness of grinding. Unless reagents such as grinding aids or dispers~mts are added, the fine particles can reagglonlerate and prevent a decrease in average
148
S. Chander : Colloids' Surlhct, s A: Plo'sit'ocht,m, Eng. A~l~ects 133 (1998) 143 150
particle size upon prolonged grinding. Grinding aids are often used to avoid such problems in grinding of materials to ultra fine sizes. The grinding aids are reagents that adsorb at various interfaces and alter interparticle forces. A variety of reagents have been found to be effective as grinding aids [10-12]. In preparation of suspensions from powders prepared by dry methods, the initial step is the wetting of powders. Some materials, such as pigments and pharmaceutical powders, are not easily wetted by water and, therefore, wetting agents are needed to promote transfer of particles from air into the liquid phase. Since dry powders are often
aggregated, a deagglomeration step is also required. Experience shows that chemical means of wetting and dispersion are more effective than mechanical methods as the size of particle decreases.
4. A systems approach--a hierarchy system for colloldal dispersions A hierarchy system, presented in Fig. 5, is proposed in this article to rationalize the various type of interactions that occur in a concentrated dispersion. The importance of such an integrated
HIERARCHYSYSTEMFOR COLLIODALDISPERSIONS
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I Level1: Bulk Pmptrtles & Hydrodynamics | Particleprope;lk)s(s~edistribution, density,SOlubility),reegenltypeand concentration,agitationintensity Fig, 5. A hierarchy, s.vstcm for c~)ltoidal dispersions.
S. Clumder / Colloids SurfiJces A." Physk'ochen Eng. Aspects 133 (1998) 143 150
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approach to understanding the system behavior becomes clear if one is interested in determining and predicting the effect of both the physical variables (such as rate of mixing, particle size, particle density) and the chemical variables (such as reagent type and concentration) on properties of the suspension. The system properties, such as rheology and stability in the case of dispersions, and adhesion to substrates and density in the case of coatings, depend on a large number of subprocesses which are separated into different levels in the hierarchy system presented in Fig. 5. The effect of changes in the above variables becomes complex because different variables effect rations sub-processes in disparate ways. To control the properties of a suspension at Level 5, tot example, one may have to adjust the Level 1 parameters of particle size distribution, reagent type and concentrati'~n~ or agitation intensity. Such changes will
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affect interfacial interactions at Level 2, which might influence multi-phase interactions at Level 3 and interactions between two particles or a particle and a substrate at Level 4. The interparticle forces will eventually influence multi-particle interaction at Level 5, Thus, the interactions at a lower level affect properties of the system at higher levels in an orderly manner. To illustrate the difficulties in establishing property-performance relationships, some selected results are presented in Figs. 6 and 7. The effect of pH on viscosity and electrophoretic mobility of alumina is given in Fig. 6. The sharp increase in viscosity between pH 6 and 7 cannot be explained by the chtssical DLVO theory alone. The results in Fig. 7 also illustrate the problems in relating zeta potential to turbidity. The turbidity decreased,
150
S, (~lander : C~JI/ohL~ Su(/bce,v .,l: Plo'sk'ochem. Eng. /ispects 133 ( 1998~ 143 150
w h e r e a s the z e t a p o t e n t i a l r e m a i n e d c o n s t a n t f o r p H 2 - 6 . T h i s b e h a v i o r is not e x p e c t e d b a s e d on the classical D L V O theory. P u g h [ 14], in r e v i e w i n g the results o f L a n g e a n d M i l l e r [7], c o n s i d e r e d t h a t the t u r b i d i t y c a n be c o r r e l a t e d to zeta p o t e n tial. O b v i o u s l y sucb c o r r e l a t i o n s a r e q u a l i t a t i v e in n a t u r e .
5. Summary S e v e r a l issues r e g a r d i n g c o n c e n t r a t e d suspensions a r e reviewed in this article. E v e n t h o u g h m a n y studies h a v e been m a d e to i n v e s t i g a t e c o n c e n t r a t e d o r d e n s e slurries, several g a p s exist b e t w e e n t r a n s f e r o f k n o w l e d g e f r o m o n e a r e a into a n o t h e r . In m a n y s i t u a t i o n s , g e n e r a l t h e o r i e s are a v a i l a b l e for i n d i v i d u a l s u b - p r o c e s s e s b u t not for the system as a whole, m a k i n g it difficult to predict p e r f o r m a n c e o f a system o f c o n c e n t r a t e d suspensions f r o m p r o p e r t i e s o f tbe parti~:les a n d the m e d i u m . In m a n y cases c a u s e a n d effect r e l a t i o n ships are not c l e a r , p e r h a p s becau:;e the c o u p l e d el'feet o f p h y s i c a l a n d c h e m i c a l v a r i a b l e s has not bccn fully cstablishcd.
References 111 R.H Oltcwill. in: tW. (]ood~in ~Ed.). Concentrated Dispersions. No. 43. Royal Socicl3 of Chemistry, London. 1982, Chapler 9. [2] II..H Oltewill. in: RII. Ottewilk J.W. Goody, in (Eds.). Concentrated l)ispersions, I. I:tlndamental ('onr;iderations
in Science and Technology, of Polymer Colloids, vol. IL Martinus Nijhoff, Boston. 1983. p. 503. [31 Th.F. Tadros. Control of the properties of suspensions, Colloids Surf. 18 (1986) 137 173. [4] F,M. Auzerais, R. Jackson. W.B. Russel. The resolution of shocks and the effect of compressible sediments in transient settling. J. Fluid Mech. { 1988)437 462. [5] A. Bleicr, C.G. Westmoreland. Effects of adsorption of polyacrylic acid on Ihc stability of a-AI:O~, m-ZrO2, and their binary suspension system~, in: Y. Ania, B.M, Moudgil. S. Chander IEds.t, haerl2lcial Phenomena in Biotechnolog~, and Materials Processing, Elsevier. Amsterdanl. 198g, pp. 217 236. [6] W. Shih. S.I. Kim. W.Y. Shih. C.H. Schilling, I.A. Aksay. Consolidation of colhfidal suspensions. Mater. Res. Soc. Symp. Proc. 180 (19911) 167 172. 171 F.F. Lange, K.T+ Miller. Pressure lihration: consolidation kinetics and mechanics, Am Ceram. Soc. Bull. 66 1101 (1987) 1498 15114. 181 W.J. Frith, J. Mex~is, T,A. Stri~enx. Rhcology of concentrated suspensions, Powder 7~:chnoL 51 ( 19871 27 34. [9] L.A. Mondy, A.L. Graham, Rheology and microslructure of concentrated suspensions, in: B.J.J. Zelinnski, C.J. Ilrinker, I).E Clark, D.R Ulrich (Eds.L Better Ceramics Through Chemislr}, Maler. Res. Soc. Syrup. Proc 180 111)90) 173 184 [101 I I El-ShalL Grinding aids. in: P. Somasundaran, B. Moudgil I Eds.L Reagenls in Mineral Industry. Dckkcr. Nc~ York It)g7, pp 159 177. [111 R,R. Klimpel, (irinding aids based on slurry theology, ill: P. Somasundaran. B. Moudgil ( Etls L Reagents in Mineral Induslrx, Dckker, New York 1~,~87.pp. 179 lti4. [121 R.R, Klimpcl. R.D. llan~en. Chemislry ~1 mineral slurry rheology ct>ntrol grinding aids, Miner. Metalh Process. 6 IttS~:ll 55 43. [131 li.M. DeLiso, .,\.s. Rao, wl.'. Cannon. Elcctrokinctic behavior of AI:Oj and ZrO, powders in dilute and conccnIraled aqncotls tli~pcrsions. Adx, Ceram. 21 11987) 525 535. [141 R.J. Pugh, I)ispersitm and stability of ceran'~ic powders in liquids, in: RJ. Pugh. L. Bergstrom I Eds.), Surlace and Collokl Uhemi~try m Advanced Ceramics Processing, Dckkcr, New York. I t,i94. ¢,'haplcr 4.
AND ELSEVIER
Colloids and surf~.... A: Physicochemic~d~mdEngineeringAspects 13311998) 143 150
A
~UR~AC~
Challenges in characterization of concentrated suspensions S. C h a n d e r 115 th,.vler Building. Penn Stare Unirersitr. University Park PA 168¢)2. USA
Accepted I April 1997
Abstract With a decrease in perticle size below I rLm Ihe role of surfaces and interlhcial phenomena dominates the properties of powders in liquids. A knowledge of properties of the system is often desired to develop predictive strategies to control the state of dispersion and aggregation of powders. To obtain the desired stability and rheology of suspensions, an adjustment of both physical and chemical variables might be reqnired. The success of such an approach depends on the ability to predict correctly the system response fron't characteristics of the powder and suspending medium. Several traditiomd methods of characterization depend upon measurements in dilute suspensions, whereas most applications deal with processing and transport of dispersions at htrge particle loading (percent solids). Challenges in rchning properties measured in dihae suspensions to predict lhc behavior of concentrated suspensions will be discussed. golh thermodynamic or equilibrium, and kinetic or rate elfects are considered. ~o 1998 Elsevier Science B.V. KO'wordw Concentrated snspensions; Characterization: Dynamic properties: Stability
I. Concentrated suspensionsIdefinitions The terlrl "concentrated suspension" is often used without a clear definition. In many cases the practical definition is user-dependent and not alw',tys usefal across different fields of interest. At one extreme, n suspension may be cotlsidered dilute if the thermal motion of the particle predominates over the effect imposed by interparticle forces [ 1,2]. As a result, the particle translational motion is large compared to the range in which interparticle forces are significant. In dilute suspensions, colloid properties can be described in terms of two-body inter;~ctions between a pair of particles. In these "'dilute" systems particles move independently and they do not "~see'" each other except for a chance collision. Such systems are seldom of prnetieal interest, however. At the other end of the spectrum is the so-called "'ordered" suspension in which particles occupy specific sites with respect 0927-7757;9s sI9.110t, 1998Elsevier:~cienceB.V. All rights reserved. PII $1t927-7757197 )tilt 134-9
to each other. S'~c~: suspensions are conveniently referred to as "'solid" suspensions. The properties of such suspension,~ could be time invariant if interparticle forces do not change with time. In between the above extreme cases of "'dilute" and "'solid" suspensions are systems which are loosely defined as "'concentrated". In these systems, which are of most practical importance in the industry, particle interactions are many-body in nature and the translational motion of the particles is restricted [3]. The particles "'see" each other within a short time scale when compared with "'dilute" suspensions. The properties of such systems are time-dependent showing both spatial and temporal distributions. Theoreticnl!y. the radial distribution of particles around a central particle can be used to describe microstructure in ~uch suspensions. Determination of such a distribution is not a trivial task, however. In many practical applications, where the aim is to control various properties o f
144
,~ ( 7la~tder ('o]loi~Ll"StctJktct.s A: Ph.rsh'l~rhtwt, Erie. A~¢cts 133 ~ 199~) 143 15(1
the system, the goal of an investigator is to relate particle properties to macroscopic properties, such as osmotic pressure, stability or rheology. The usual expression for mean interparticle spacing H in a suspension is
where D is particle diameter, ~ is volume fraction, and ~,, is volume fraction at maximum packing. For such a calculation, all particles are assumed to be spherical and of same size. The interpartiele spacing H for particle of various diameters is plotted as a function of volume fraction in Fig. I using the above relation. It can be seen that the interparticle spacing is less than the particle diameter in suspensions of most practical interest. Tile value of ~,~ depends on the packing of particles in the suspension. As a limiting case, if the particles are arranged ill a close-packing structure, for example face-centered cubic, the value of ~Pm is 0.74 and the value of ¢]J at which the distance of separation between nearest neighbors is equal to particle diameter is 0.093. On the other hand, if the particles are arranged in a simple cubic arrangement in the liquid, the wduc of q~ for a similar interparticle spacing is 0.066. This difference arises because tile wdue of q~m ill a simple
cubic arrangement is 0.524. In other words, the average distance of separation between particles is equal to the particle diameter in a range of volume fractions, which is a fnnction of structure of the suspension. Further differences between the definition of dilute and concentrated suspensions could arise due to the particle shape effects and colloid interactions between the particles. The effect of colloid forces can be incorporated in the case of "'stable" suspensions by considering a modified particle diameter based on the "'sphere of influence" of the particle. To define the sphere of influence a knowledge of interparticle lbrccs is required, however. Differences in structural arrangement of particles in a suspension could arise when attractive and weakly repulsive Ibrces are present between the particles. In such a case the arrangement of particles in the suspension becomes a f.mction of time and is determined by kinetics of coagulation. Thus, the definition of dilute and concentrated suspensions is a ftmction of the arrangement of particles in the suspension, which in turn depends on interparticle forces. The effect of interparticle forces are discussed in the paragraphs that lbllo~. It was discussed in the previous paragraph that, at volume fractions gceuter than a critical value, a transhtting particle will collide with the particle in
-3 o o
i
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ParUefe Diameter, gm
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0,6
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Fig. I. The dishlnce of .~¢pLIri~tiol'z I I cm hl~t~.q,¢¢n p~lrljuql~s as ~t I'tlll~|ion ~f "~olUIl1¢ fra¢lk~n ,p of solids klzKI p;IrliL'l¢ ~,jZu'. §~m iS Ihe vohlme I'r;iction ~d" solids when Ih¢ panb;lCs touch I'lCjghborhlg parlicl¢~.
s, ('bander ; ('olloM.v Surfitce~" A. ?'l)wtcochent Eng. Aspects 133 (1998) 143-150
its immediate vicinity. A force will be transmitted from one particle to another after such an event. The magnitude of such a force would follow rules of momentum transfer but will also depend on mutual interactions between the particles. Electrical double layer interactions, van der Waals forces and solvation effects are known to influence t~roperties of concentrated suspensions, but their effect is rarely incorporated in quantitative theories of macroscopic properties of such systems. Definite forms of momentum balances, wflid over a whole range of particle sizes, solids concentration or particulate density, and interparticle interactions are not available. All existing attempts to lbrmulate a theory usually involve ad hoc assumptions, some of which may be controversial. At volume fractions corresponding to interparticle distances smaller than the particle diameter, the probability of multi-body particle interactions increases and the forces of interacti~,n between particles play a dominant role in determining the system properties. Such interactions cannot be ignored for a "+concentrated" suspension, however. Auzerais et hi. [4] presented a detailed model of the settling of concentrated snspensions, but had to linfit their calculations to two extreme cases: the hard sphere model, and the flocculated model. The effect of distance-dependent magnitude of interparticlc forces could not be taken into account. Although used as the most connnou control variable, the volume fraction alone is not sufficient to describe the properties of a concentrated suspension. To illustrate this limitation, consider the coagulation time constant (defined as the time required for a system to decrease the number of particles to half its initial valuet as a function of volume fraction for particles of various sizes. The values are given in Fig. 2 for a rapidly coagulating system. The coagulation time constant can vary from a few milliseconds to several hours, depending on particle size and volume fraction. Thus, the definition of a concentrated suspension must incorporate, at the very least, volume fraction, particle size (distribution), and interparticle forces. 2. Characterization ufa disperse system Adequate characterization of a disperse system is important if one needs to develop ways to
145
predict system properties and relate them to performance. A system of disperse particles might be characterized by properties of the disperse phase(s), continuous phase, interfacial properties and the colloid properties. A list of these properties is given in Table I. Although several methods are available to determine various properties under isolated conditions, difficulties remain for measurements in concentrated suspensions. As an example, in many industrial systems the state of aggregation of primary particles is most difficult to control and measure. In principle, the aggregates can be characterized by the size distribution, density, strength and rate of their formation. However, most modern methods for determining size distributions do not distinguish between aggregates of fine particles and course particles. Since disperse, continuous and interracial properties can be measured routinely by traditional methods, further discussion in this article is limited to stability and rheology. 2. I. Stabili(v
Methods of characterizing stability of concentrated dispersions have not been standardized, and a large variation in techniques and methodology exists in the literature. The simplest way to determine stability is to measure sediment volume, sediment density or sediment height
14fi
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Eng. A.~7}ects 133 ( 199,~ 143 150
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Table 1 Paralnet¢ls for ch~lraClerizinga s3~tenl of dispersed pill'lides I)is~.rse phase properties
Size dislribution Particle shape I)ensil,, Surl~lc¢ ¢llcrgy nolntll~cll¢il~
Several disperse phast's
Solid i1;tl Iiclt.'s or liquid droplets, each aith propcrti,::, lisled M)ow' Relative size of dispersed phase o1' difllczcnl /nalcrials
Conlin uou.,,; pha~'
Aq tl¢Otls N(lll-aqucous Dissolved s IIbMa IIc¢:',
Interracial proptrrtit'.~
EIcclriu~dtmbl¢-Ia3er zt21ll pOlt211li~d Adsorplion density Packing of nlolectlle~ ill Ih¢ adsorbed la.~cr Thickness of adsorbed layer
Colloid properlit~
Percent solids Stabilil} Rhcoh~gy l.ight st-ant:ring
riot nnifornl and the sediment migllt have a nonnnilbrm density. The results after consolidation in a centrifttge are given in Fig. 3 [6] as an illustralion. Ahhough additional information about the properties of the system could he obtained from measuring the rate of settling, such tests are not ordinarily pertbrmed tbr eoncenlrated suspensions and the available data are meager, Pressure liltration is another method used by some investigators to describe the settling behavior of suspensions [7]. Thc most c o m m o n approach is to measure equilibrium cake height as a fimction of pressure. The results after consolidation by pressure filtration are given Fig. 4 [6]. Important differences between the results of centrifugal settling and pressure filtration are noticeable, hi centrifugal settling tile packing density varies linearly witb pressure when the two quantities are plotted on logarithmic scales. In contrast, the packing density wtried with the logarithm of the applied pressure in pressure filtration. Obviously, important differences must exist in the two cases. The reasons for such differences were not discussed by the investigators and are not obvious. In centrilugal settling the pressure ranges from about a few deci- to se~'eral kilo-pascals, whereas it, pressure
S. Chmuh'r / ('olh#d~ SurJb 'es A." Ph.!'sk'ochcm. Eng. Aspe~'rs 133 (199t¢) 143-150 10 2
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•
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(MPn)
Fig. 3. Packing density tit ~;teady simile b~ ccntrifugation ils ~I function o f the me~lD pressure ['~r micrometer-:,izcd alumilm ~lnd n~ln~inclcr-siztrd boehn'fitc suspensions [6 I.
filtration it ranges from a few deci- to several mega-pascals, The packing behavior of particles in the suspension could change with increase in pressure but the type of change that could occur rcntaius to be established. 2.2. D t'mu,icpr~qwrtie.~
Rheok~gy properties c~m b~. u~.ed to dc~cribe the dynamic properties of concentrated suspensions under flow conditions. These properties can be
147
investigated using steady state, constant stress (creep) or oscillatory measurements [8]. Rheology properties of the suspensions vary considerably with change in interparticle forces. As a result, they are often grouped into different categories based on hard sphere interaction, double layer repulsion, steric stabilization, weak attraction {weakly flocculated suspensions), and strong attraction {strongly flocculated suspensions). Such a sub-division is obviously arbitrary and arises from the lack of a rigorous theory that can incorporate interaction between particles into rheology theories. Other difficulties arise in determination of rheology properties. For non-Newtonian systems, the properties often depend on history of the dispersion and segregation of particles in the test cell. Using an NMR imaging technique, Mondy and Graham [9] demonstrated that a 60 vol.% suspension containing bidisperse spheres segregated into concentric cylinders with alternating coarse and fine particles. Similar problems could arise in a rheology test cell if the suspension contains a wide distribution of particle sizes. Slip near the walls of the test cell is another well recognized major problem in measuring rheology properties of dense slurries.
3. Preparation of dispersions 8O ~'~
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=~ 60
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•
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Preparation of a dispersion l¥om a dry powder is the first step in many practicab-applications and laboratory investigations. Though technically important, this feature if often ignored in many discussions involving concentrated suspensions. Dispersions can be prepared either by precipitation methods or by comminution of coarse particles. Although a detailed discussion of either of these topics is beyond the scope of this article, a brief commentary is included because the dispersion properties play an important role in both cases. In comminution, production of fine particles could result in an increase in viscosity of the suspension, decreasing stress transfer and effectiveness of grinding. Unless reagents such as grinding aids or dispers~mts are added, the fine particles can reagglonlerate and prevent a decrease in average
148
S. Chander : Colloids' Surlhct, s A: Plo'sit'ocht,m, Eng. A~l~ects 133 (1998) 143 150
particle size upon prolonged grinding. Grinding aids are often used to avoid such problems in grinding of materials to ultra fine sizes. The grinding aids are reagents that adsorb at various interfaces and alter interparticle forces. A variety of reagents have been found to be effective as grinding aids [10-12]. In preparation of suspensions from powders prepared by dry methods, the initial step is the wetting of powders. Some materials, such as pigments and pharmaceutical powders, are not easily wetted by water and, therefore, wetting agents are needed to promote transfer of particles from air into the liquid phase. Since dry powders are often
aggregated, a deagglomeration step is also required. Experience shows that chemical means of wetting and dispersion are more effective than mechanical methods as the size of particle decreases.
4. A systems approach--a hierarchy system for colloldal dispersions A hierarchy system, presented in Fig. 5, is proposed in this article to rationalize the various type of interactions that occur in a concentrated dispersion. The importance of such an integrated
HIERARCHYSYSTEMFOR COLLIODALDISPERSIONS
~
~
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I Level1: Bulk Pmptrtles & Hydrodynamics | Particleprope;lk)s(s~edistribution, density,SOlubility),reegenltypeand concentration,agitationintensity Fig, 5. A hierarchy, s.vstcm for c~)ltoidal dispersions.
S. Clumder / Colloids SurfiJces A." Physk'ochen Eng. Aspects 133 (1998) 143 150
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approach to understanding the system behavior becomes clear if one is interested in determining and predicting the effect of both the physical variables (such as rate of mixing, particle size, particle density) and the chemical variables (such as reagent type and concentration) on properties of the suspension. The system properties, such as rheology and stability in the case of dispersions, and adhesion to substrates and density in the case of coatings, depend on a large number of subprocesses which are separated into different levels in the hierarchy system presented in Fig. 5. The effect of changes in the above variables becomes complex because different variables effect rations sub-processes in disparate ways. To control the properties of a suspension at Level 5, tot example, one may have to adjust the Level 1 parameters of particle size distribution, reagent type and concentrati'~n~ or agitation intensity. Such changes will
10 ~ 2
i
I
I"
4
6
8
t4n
10
n 12
pH Fig. 7. The zel;i potential a n d turbidity o f alumina as a function of p H [ 141.
affect interfacial interactions at Level 2, which might influence multi-phase interactions at Level 3 and interactions between two particles or a particle and a substrate at Level 4. The interparticle forces will eventually influence multi-particle interaction at Level 5, Thus, the interactions at a lower level affect properties of the system at higher levels in an orderly manner. To illustrate the difficulties in establishing property-performance relationships, some selected results are presented in Figs. 6 and 7. The effect of pH on viscosity and electrophoretic mobility of alumina is given in Fig. 6. The sharp increase in viscosity between pH 6 and 7 cannot be explained by the chtssical DLVO theory alone. The results in Fig. 7 also illustrate the problems in relating zeta potential to turbidity. The turbidity decreased,
150
S, (~lander : C~JI/ohL~ Su(/bce,v .,l: Plo'sk'ochem. Eng. /ispects 133 ( 1998~ 143 150
w h e r e a s the z e t a p o t e n t i a l r e m a i n e d c o n s t a n t f o r p H 2 - 6 . T h i s b e h a v i o r is not e x p e c t e d b a s e d on the classical D L V O theory. P u g h [ 14], in r e v i e w i n g the results o f L a n g e a n d M i l l e r [7], c o n s i d e r e d t h a t the t u r b i d i t y c a n be c o r r e l a t e d to zeta p o t e n tial. O b v i o u s l y sucb c o r r e l a t i o n s a r e q u a l i t a t i v e in n a t u r e .
5. Summary S e v e r a l issues r e g a r d i n g c o n c e n t r a t e d suspensions a r e reviewed in this article. E v e n t h o u g h m a n y studies h a v e been m a d e to i n v e s t i g a t e c o n c e n t r a t e d o r d e n s e slurries, several g a p s exist b e t w e e n t r a n s f e r o f k n o w l e d g e f r o m o n e a r e a into a n o t h e r . In m a n y s i t u a t i o n s , g e n e r a l t h e o r i e s are a v a i l a b l e for i n d i v i d u a l s u b - p r o c e s s e s b u t not for the system as a whole, m a k i n g it difficult to predict p e r f o r m a n c e o f a system o f c o n c e n t r a t e d suspensions f r o m p r o p e r t i e s o f tbe parti~:les a n d the m e d i u m . In m a n y cases c a u s e a n d effect r e l a t i o n ships are not c l e a r , p e r h a p s becau:;e the c o u p l e d el'feet o f p h y s i c a l a n d c h e m i c a l v a r i a b l e s has not bccn fully cstablishcd.
References 111 R.H Oltcwill. in: tW. (]ood~in ~Ed.). Concentrated Dispersions. No. 43. Royal Socicl3 of Chemistry, London. 1982, Chapler 9. [2] II..H Oltewill. in: RII. Ottewilk J.W. Goody, in (Eds.). Concentrated l)ispersions, I. I:tlndamental ('onr;iderations
in Science and Technology, of Polymer Colloids, vol. IL Martinus Nijhoff, Boston. 1983. p. 503. [31 Th.F. Tadros. Control of the properties of suspensions, Colloids Surf. 18 (1986) 137 173. [4] F,M. Auzerais, R. Jackson. W.B. Russel. The resolution of shocks and the effect of compressible sediments in transient settling. J. Fluid Mech. { 1988)437 462. [5] A. Bleicr, C.G. Westmoreland. Effects of adsorption of polyacrylic acid on Ihc stability of a-AI:O~, m-ZrO2, and their binary suspension system~, in: Y. Ania, B.M, Moudgil. S. Chander IEds.t, haerl2lcial Phenomena in Biotechnolog~, and Materials Processing, Elsevier. Amsterdanl. 198g, pp. 217 236. [6] W. Shih. S.I. Kim. W.Y. Shih. C.H. Schilling, I.A. Aksay. Consolidation of colhfidal suspensions. Mater. Res. Soc. Symp. Proc. 180 (19911) 167 172. 171 F.F. Lange, K.T+ Miller. Pressure lihration: consolidation kinetics and mechanics, Am Ceram. Soc. Bull. 66 1101 (1987) 1498 15114. 181 W.J. Frith, J. Mex~is, T,A. Stri~enx. Rhcology of concentrated suspensions, Powder 7~:chnoL 51 ( 19871 27 34. [9] L.A. Mondy, A.L. Graham, Rheology and microslructure of concentrated suspensions, in: B.J.J. Zelinnski, C.J. Ilrinker, I).E Clark, D.R Ulrich (Eds.L Better Ceramics Through Chemislr}, Maler. Res. Soc. Syrup. Proc 180 111)90) 173 184 [101 I I El-ShalL Grinding aids. in: P. Somasundaran, B. Moudgil I Eds.L Reagenls in Mineral Industry. Dckkcr. Nc~ York It)g7, pp 159 177. [111 R,R. Klimpel, (irinding aids based on slurry theology, ill: P. Somasundaran. B. Moudgil ( Etls L Reagents in Mineral Induslrx, Dckker, New York 1~,~87.pp. 179 lti4. [121 R.R, Klimpcl. R.D. llan~en. Chemislry ~1 mineral slurry rheology ct>ntrol grinding aids, Miner. Metalh Process. 6 IttS~:ll 55 43. [131 li.M. DeLiso, .,\.s. Rao, wl.'. Cannon. Elcctrokinctic behavior of AI:Oj and ZrO, powders in dilute and conccnIraled aqncotls tli~pcrsions. Adx, Ceram. 21 11987) 525 535. [141 R.J. Pugh, I)ispersitm and stability of ceran'~ic powders in liquids, in: RJ. Pugh. L. Bergstrom I Eds.), Surlace and Collokl Uhemi~try m Advanced Ceramics Processing, Dckkcr, New York. I t,i94. ¢,'haplcr 4.